This paper studies the properties of convexity (concavity) and strategic complements (substitutes) in network formation and the implications for the structure of pairwise stable networks. First, different definitions of convexity (concavity) in own links from the literature are put into the context of diminishing marginal utility of own links. Second, it is shown that there always exists a pairwise stable network as long as the utility function of each player satisfies convexity in own links and strategic complements. For network societies with a profile of utility functions satisfying concavity in own links and strategic complements, a local uniqueness property of pairwise stable networks is derived. The results do neither require any specification on the utility function nor any other additional assumptions such as homogeneity.

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dc.language.iso

eng

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dc.publisher

Inst. of Mathematical Economics, IMW Bielefeld

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dc.relation.ispartofseries

Working papers // Institute of Mathematical Economics 423

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dc.subject.jel

D85

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dc.subject.jel

C72

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dc.subject.jel

L14

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dc.subject.ddc

330

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dc.subject.keyword

Networks

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Network formation

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Game theory

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Supermodularity

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Increasing differences

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Stability

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Existence

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Uniqueness

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dc.subject.stw

Soziales Netzwerk

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dc.subject.stw

Nutzenfunktion

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dc.subject.stw

Spieltheorie

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dc.subject.stw

Gleichgewichtsstabilität

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dc.subject.stw

Theorie

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dc.title

Convexity and complementarity in network formation: Implications for the structure of pairwise stable networks